<p>By extending the results obtained by D. E. Knuth (1986), a parallel unordered coding scheme with 2/sup r/ information bits is described. Balanced codes in which each codeword contains equal amounts of zeros and ones, with r check bits and up to 2/sup r+1/-(r+2) information bits, are constructed. Unordered codes with r check bits and up to 2/sup r/+2/sup r-1/-1 information bits are designed. Codes capable of detecting 2/sup r-1/+(2/sup r//2)-1 unidirectional errors using r check bits are also described. A review of previous work is presented.</p>